4x=(6x)(5x-14)

Solution for 4x=(6x)(5x-14) equation:

4x=(6x)(5x-14)

We move all terms to the left:

4x-((6x)(5x-14))=0


We calculate terms in parentheses: -(6x(5x-14)), so:

6x(5x-14)

We multiply parentheses

30x^2-84x

Back to the equation:

-(30x^2-84x)


We get rid of parentheses

-30x^2+4x+84x=0

We add all the numbers together, and all the variables

-30x^2+88x=0

a = -30; b = 88; c = 0;
Δ = b2-4ac
Δ = 882-4·(-30)·0
Δ = 7744
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7744}=88$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(88)-88}{2*-30}=\frac{-176}{-60}
=2+14/15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(88)+88}{2*-30}=\frac{0}{-60}
=0
$